1. Field of Invention
The field is structural members for use in building construction, and in particular geodesic domes and strut attachment hubs for use in such domes.
2. Prior Art
The term “geodesic” means the shortest line between two points on any geometrically defined surface, and a geodesic structure is one made of structural elements that are held in place by a collection of hubs. I.e., the ends of such structural elements are attached by strut attachment hubs; the entire arrangement usually forms a geodesic dome.
In U.S. Pat. No. 3,844,664 (1974), Hogan shows a disc-like hub for an icosahedron (20-sided) structure. The attachment points for Hogan's struts are all equidistant from the center of the hub.
In U.S. Pat. No. 4,534,672 (1985), Christian shows a hub for a geodesic dome with wooden struts. The hub has six connection points, each comprising a pair of metal straps that sandwich the end of a strut. The six pair of straps are joined to each other at their inner ends. The straps each have a hole for holding a bolt that is inserted through the straps and the strut. The straps are arranged to accommodate struts of three different lengths, A, B, and C.
Reber, in U.S. Pat. No. 4,703,594 (1987), shows a hub with radially equidistant connection points; therefore struts of differing lengths are required by his design.
Ziegler, in U.S. Pat. No. 5,230,196 (1993), shows a polyhedron construction system with a hub for connecting cables and struts.
In U.S. Pat. No. 5,996,288 (1999), Aiken shows a geodesic dome with a hub for wood struts having connection points equally spaced from the center.
In U.S. Pat. No. 6,296,415 (2001), Johnson et al. show a hub for holding the struts of a structure where the ends of the struts are ball-shaped. The hub has sockets for holding the ball-ends. The distance between the ends of the balls of coaxially-aligned struts can be adjusted to accommodate different fabrics laid over the struts by rotating the hub.
In published U.S. patent application 2004/0158999, Trantow shows struts for geometric modeling with end connectors.
The prior-art hubs described above all provide structural integrity in structures constructed of struts. In the case of geodesic domes, struts of differing lengths have previously been fitted to hubs at a series of connection points, each of which is located at the same distance from the center of the hub.
3. Prior-Art—Geodesic Structures—FIGS. 1 through 3
Geodesic domes are well known in the art. The underlying principle in the construction of such domes is the subdivision of spherical surfaces into triangles or other geometric figures. This is usually done by projecting the sides of a polyhedron (multiple-sided figure) onto the surface of a sphere circumscribed about the apexes of the polyhedron. The polyhedron usually is usually one of the five Platonic solids, namely a convex, regular polyhedron with four, six, eight, twelve, or twenty sides, i.e., a tetrahedron, a cube, an octahedron, a dodecahedron, or an icosahedron. This can be achieved by several methods with varying results. In general, the strongest structures are made using a polyhedron with equilateral triangular sides. Thus the cube and dodecahedron, which don't have equilateral triangular sides, are less important in structural design than the three remaining Platonic solids.
As stated, all of the apexes of the polyhedron lie on the surface of a circumscribed sphere. When the edges of the tetrahedron, octahedron, or icosahedron are projected onto the surface of the sphere they define great circle arcs. Careful examination reveals that any further subdivisions and projection of these solids (which, as stated, have equilateral triangular sides) onto a sphere creates isosceles triangles (two equal-length sides) and not the desired equilateral triangles (three equal-length sides). This can more readily be understood by examining a group of equilateral triangles, each sharing an edge with the next and clustered about a single point. Three equilateral triangles clustered thusly form a tetrahedron. Four clustered thusly form one half of an octahedron. Five form one portion of an icosahedron, but when six are arrayed in this manner they are planar, and when projected onto the surface of a sphere it becomes clear that some of the edges must elongate before they can conform to the spherical curvature. I.e., the projected edges of the solid with equilateral triangular sides have differing lengths on the sphere.
However it is desirable for the lengths of the projected geodesic edges to be as equal as possible. There are two reasons for this. First is the matter of structural efficiency: if the same cross section is used for all elements, that cross section must be sufficient for the strength of the longest of those elements and therefore more substantial than required for the shorter elements. This leads to an over building of some components and a consequent inefficiency of material utilization.
The second reason for uniformity of edge lengths is important is for simplification of construction. This is especially true in portable structures that must be assembled and disassembled frequently. It becomes even more important when those who are to assemble the domes are not trained specifically in their construction. Military tents are frequently set up by untrained infantry personnel, and emergency relief tents are frequently set up by the very civilians who must use them for shelter. Thus it can be seen that it is highly desirable to reduce the complexity of this type of geodesic dome.
In U.S. Pat. No. 2,682,235 (1954), Fuller shows the construction of a geodesic dome. Struts of differing lengths are used in the assembly of the dome.
FIG. 1 of the drawings shows a prior-art icosahedron 100. As described in the Fuller patent, supra, icosahedron 100 is a starting polyhedron having 20-sides with 20 equilateral triangles 105, with twelve vertices, and 30 sides. He then “explodes” this figure within an imaginary sphere 200 (FIG. 2), thereby projecting the sides of triangles 105 onto sphere 200, yielding a number of curvilinear triangles 105′. The curved sides of triangles 105′ lie on great circles on sphere 200. Fuller's method for subdividing icosahedron 100 into triangles is referred to as the “Alternate Method” by those skilled in the art of geodesic structure design. There are other methods, including the Triacon Method, discussed infra.
FIG. 3 shows a portion of Fuller's icosahedron 100 of FIG. 1. The lines forming equilateral triangles 300 intersect at points 310. The intersections of lines A-B-C forming triangles 300 contain five lines.
In his structure, Fuller refers to the lines forming the triangles as struts. He approximates sphere 200 (FIG. 2) with a large number of struts that are joined at their vertices by hubs. The nearer the structure comprising struts and hubs approximates a sphere, the stronger the structure will be.
In Fuller's structure, each of triangles 105 is subdivided further, or tessellated, into smaller triangles 300 (FIG. 3). For example, triangle A-B-C is subdivided into four triangles 300. The lines forming triangles 300 and 105 intersect at points 305. Each of these intersections contains six lines. The term frequency is used to indicate the degree of tessellation of the original, icosahedral triangle 105. A frequency of four is shown in FIG. 3, meaning that the original triangle is divided into four smaller triangles. Additional tessellations can be performed, yielding many more triangles. Fuller notes that with a frequency of four, five different strut lengths are required to build a dome. A frequency of eight requires 16 different strut lengths, while a frequency of 16 requires 56 different strut lengths.